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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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Scale matters.

L G Margolin1

  • 1Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA len@lanl.gov.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 21, 2018
PubMed
Summary

This study extends the Chapman-Enskog approximation for fluid dynamics, developing a new hydrodynamic model applicable to non-equilibrium flows. The proposed model generalizes local thermodynamic equilibrium using a novel velocity probability distribution function (PDF).

Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Navier-Stokes equations are limited to near-equilibrium flows with small gradients.
  • Existing models struggle with flows far from thermodynamic equilibrium.

Purpose of the Study:

  • To extend the Chapman-Enskog approximation for non-equilibrium fluid flows.
  • To derive a generalized hydrodynamic model beyond local thermodynamic equilibrium.

Main Methods:

  • Averaging the velocity probability distribution function (PDF) in both coordinate and velocity phase spaces.
  • Deriving a gradient-dependent PDF as a first-order generalization of local thermodynamic equilibrium.
  • Integrating the derived PDF to formulate a new hydrodynamic model.
Keywords:
coarse-grainingfinite scalehigh Reynolds number

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Main Results:

  • A novel velocity probability distribution function (PDF) dependent on gradients was derived.
  • A new hydrodynamic model was formulated by integrating the generalized PDF.
  • The properties of the model and its relation to computational fluid dynamics (CFD) discrete equations were discussed.

Conclusions:

  • The proposed extension offers a pathway to model non-equilibrium fluid dynamics.
  • The derived hydrodynamic model provides a first-order generalization beyond local thermodynamic equilibrium.
  • This work contributes to understanding and simulating complex fluid behaviors.